Oxygen sensors have many applications, e.g., in medical, biochemical, chemical, automotive, processing, and air quality management industries. One type of oxygen sensor is a diffusion-limited amperometric oxygen sensor for monitoring gas mixtures. These sensors are based on the operation of an electrochemical cell in a pumping mode. In particular, the oxygen concentration measurement may be governed by Faraday's law, correlating an output current with the number of oxygen ions passing through an electrolyte, and diffusion-convection partial differential equations relating an oxygen flux to gas mixture properties (e.g., O2 concentration, temperature, pressure, etc.) and/or the sensor's physical geometry and dimensions.
Oxygen sensors may be used in connection with medical ventilators, device designed to provide mechanical ventilation to patients. Ventilators are used in many settings, e.g., in intensive care medicine, home care, emergency medicine (as standalone units), and for anesthesia (as a component of an anesthesia machine). A typical ventilator may include a pressurized air source, an oxygen gas source, a series of valves and tubes, and a disposable or reusable patient circuit. A valve system (e.g., a pneumatic valve) may be actuated regularly in a controlled manner to deliver a specified air/oxygen mixture to the patient several times a minute. The patient may exhale passively to release overpressure, due to the lungs' elasticity. In some ventilators, the oxygen content of inspired gas can be set from approximately 21 percent (ambient air) to 100 percent (pure oxygen). Pressure and flow characteristics can often be set mechanically and/or electronically.
Oxygen sensors may be installed in line with the patient circuit to measure the oxygen content in the gas mixture delivered to the patient. The pressure in the patient circuit may change over time based on desired settings, ventilator dynamics, patient lung characteristics, and/or the patient's breathing effort. Under steady state pressure conditions and a fixed gas mixture, oxygen molecules may pass through a sensor aperture under a diffusion mechanism, and thus the number of oxygen molecules running through the sensor (and consequently, an output current of the sensor) may approach a stationary value. However, when the gas pressure at the sensor's input aperture is fluctuating, an additional convective dynamic gas flux may arise, causing fluctuation in the number of oxygen molecules reaching the sensor cathode. As a result, the output current of the sensor may fluctuate. With a ventilator, breathing frequencies are relatively rapid (e.g., 8 to 25 breaths per minute for normal adults, and often higher frequencies for pediatric and neonatal patients), which may result in a varying (i.e., non-steady) oxygen sensor output. Various other problems with attempting to measure oxygen concentration in gas mixtures experiencing pressure fluctuations are discussed in A. K. Demin et al., “Sensor for Measuring the Oxygen Concentration in Gas Mixtures with Unsteady Pressure, Solid State Ionics, 112 (1998) 355-359.
Certain existing approaches for calculating estimates of oxygen concentration in a non-steady pressure environment have various limitations. For example, some approaches require time-variant nonlinear diffusive-convective partial differential equations, which may be difficult to solve. In addition, numerical approximation solutions may be computationally intensive, and thus may be impractical for implementation on a ventilator platform.